中文摘要
令 λ 是在一個封閉圓盤 D 的一個複數, 和H是一個以正交基底所構成可分的希爾伯特空間 , 基底表示如下ε= {e_n:n=0,1,2,…}. 一個作用在H的有界算子T並且稱之為λ-托普立茲算子必定需要滿足以下的定義運算 <Te_(n+1) ,e_(m+1) >=λ<Te_n ,e_m >( 此處< , >表示作用在H的內積 ) 在 L^2 函數 φ~Σa_n e^inθ 伴隨著 a_n=<Te_0 ,e_n > , n>=0 , 和 a_n=<Te_n ,e_0 > , n<0 , 換句話說 ,這就稱之為T的 symbol . 這個問題的產生自然地從一個特殊的案件算子方程
S^* AS=λA+B , S 是一個作用在H空間中的一個 shift算子 ,
起著至關重要的作用範圍內尋找矩陣(a_ij ) 在 L^2 (Z)空間,解決底下的聯立方程組
{((a_(2i,2j) =p_ij+aa_ij@a_(2i,2j-1) =q_ij+ba_ij )@a_(2i-1,2j) =ν_ij+ca_ij@a_(2i-1,2j-1) =ω_ij+da_ij ) ,
對於所有的 i ,j皆屬於整數Z , 此處的 (p_ij ) ,(q_ij ) ,(ν_ij ) ,(ω_ij )是l^2 (Z)空間上的有界矩陣和a ,b ,c ,d 屬於複數C. 顯然,這也是眾所皆知的托普立茲算子,正式解決S^* AS=A的方案 , 在此篇文章中 , 此處的S 是一個單方面shift . 我們將確定譜λ-托普立茲算子與|λ|=1的有限階,和當symbols分析的C^1邊界值

Let λ be a complex number in the closed unit disk D , And H be a separable Hilbert space with the orthonormal basis , say ,ε= {e_n:n=0,1,2,…}. A bounded operator T on H is called a λ- Toeplitz operator if <Te_(n+1) ,e_(m+1) >=λ<Te_n ,e_m > (where < , > is inner product on H) The L^2 function φ~ Σa_n e^inθ with a_n=<Te_0 ,e_n> for n>=0 , and a_n=<Te_n ,e_0 > for n<0 is , on the other hand , called the symbol of T The subject arises naturally from a special case of the operator equation
S^* AS=λA+B where S is a shift on H ,
which plays an essential role in finding bounded matrix (a_ij ) on L^2 (Z) that solves the system of equations
{((a_(2i,2j) =p_ij+aa_ij@a_(2i,2j-1) =q_ij+ba_ij )@a_(2i-1,2j) =ν_ij+ca_ij@a_(2i-1,2j-1) =ω_ij+da_ij ) ┤,
for all i ,j belong Z , where (p_ij ) ,(q_ij ) ,(ν_ij ) ,(ω_ij ) are bounded matrices on l^2 (Z) and a ,b ,c ,d belong C . It is also clear that the well-known Toeplitz operators are precisely the solutions of S^* AS=A , when S is the unilateral shift . In this paper , we will determine the spectra of λ- Toeplitz operators with |λ|=1 of finite order, and when the symbols are analytic with C^1 boundary values.

論文審定書 i
中文摘要 ii
英文摘要 iii
1. Introduction 1
2.spectra of λ-Toeplitz operators with analytic symbols 4
References 8

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